Re: What do you think?

I agree that numerical methods are usually quicker and easier to use, but I still think that it's best to be algebraic whenever possible.

It's just so much nicer to be *absolutely correct* than just very accurate. Numerical methods are fine for any and all practical purposes, but to get a closed-form expression is much more pleasing.

No way to explain my way out of this. If I say I didn't notice your reply that's worse than ignoring it. Sorry for missing it.

Me too! But I do enjoy the shock value they have on some type of people who can only deal with 1,2,3,4 and the square root of 2. Such types hate numerical solutions and use words like ugly and uninspired.

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.

Re: What do you think?

Hi Bobby,

Is that way clearer for you?

The two ways are equally clear to me. For problems that lend themselves to that approach I prefer to go that way because I use my scientific calculator a lot and like to try to find concise methods to suit calculator entry if possible.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Re: What do you think?

Hi Bobby,

That is extremely close.

Yes, I should have shown fractions. I was going to but didn't think to use improper fractions, and as MIF only provides the "½" fraction symbol I opted to display my answer with the recurring digits after the decimal point. I could've tried LaTeX, but this was easier and I didn't realise the two modes gave different results.

WolframAlpha's "decimal approximation" of the fractional input is exactly the same as the one given by my calculator for which I used decimal input...up to WolframAlpha's maximum output of 3705 digits. Maybe it can display more digits, but I didn't know how to get it to do that (my calculator displays up to 5012 digits).

I wonder what the actual difference is between the correct answer and the approximations given by both WolframAlpha and my calculator.

I used Excel to solve both parts: spreadsheet for 'b' and Solver for 'a'.

Btw, your 'hidden text' label shows "b" instead of "a".

Last edited by phrontister (2010-02-24 01:39:09)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Re: What do you think?

Hi;

Thanks, I am correcting the error of a and b. Yea, sometimes Wolfram is enigmatic. The package goes to any number of digits but they are stingy on their page at times. I've written them repeatedly to provide Mathematica in its entirety at alpha, but why the heck should they listen to me.

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.

Re: What do you think?

Hi Bobby,

I spotted an error on MAlpha. After clicking "More digits" in their "Result" window the "10" disappears from the exponent reference at the end of the "Copyable plaintext" output. Not always...maybe only after a couple of clicks on "More digits", or maybe after the last-available click on it.

I've emailed them about it.

Last edited by phrontister (2010-02-24 11:58:00)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Re: What do you think?

Problem #30:

Simple probability and equation solving:

A company designs 2 new bombers. One is a 3 engine bomber and the other is a 5 engine bomber (5 engines?). Each plane can make it home with a majority of its engines operating. Each engine has a probabilty p of failure. For what values of p is the 3 engine bomber more likely to return home?

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.